3.4 Case Study
45
trapping well would reverse the ratio and, therefore, would violate Objective 1
(Q trap > Q bypass , cf. Sect. 3.4.1).
Simulations reveal that this volumetric flow rate ratio between the trapping well
and the bypass channel increases when the bypass channel length is increased and/or
the gap width is increased (which is the case for all other specifications). However,
an increase of the bypass channel length also causes an increase of the time
that a droplet requires to pass this bypass. For example, the simulation showed
that, when increasing the bypass channel length from L bypass = 4000 μm to
L bypass = 5000 μm (using a gap width of w gap = 15 μm), the time that a droplet
requires to pass a single bypass increases from 0.25 to 0.32 s (which is an increase
of 28%). This effect adds up when multiple trapping wells are cascaded. When
additionally a certain upper limit for the loading time of droplets (i.e., especially
relevant for cells) has to be fulfilled, less trapping wells can be cascaded using a
longer bypass channel, which decreases the throughput.
On the other hand, the time for droplets to be trapped can be reduced by
increasing their speed, which can be achieved by applying higher pressures at the
inlets. Using the simulator allows to test different pressures for all six specifications
and the simulator predicts that the pressure is limited by Objective 2 (cf. Sect. 3.4.1).
More precisely, too high pressures at the inlets cause too high pressure gradients
between the trapping wells and the narrow gaps so that the condition described
in Eq. 3.13 is violated. This causes the trapped droplet to be pushed through the
two narrow gaps. The simulation shows that droplet speeds can be higher for the
prototypes which have a gap width of only 15 μm. This is because a smaller gap
width increases the Laplace pressure. 1
These simulation results now allow the designer to evaluate the robustness and
performance of the different specifications. Table 3.3 summarizes the obtained
insights. Based on these results, the designer can evaluate the specifications with
Table 3.3 Robustness evaluation
ID L bypass
w gap
Possible problems
1
3000 μm 15 μm
No robust volumetric flow rate ratio (violation of
Objective 1 possible)
2
4000 μm 15 μm
–
3
5000 μm 15 μm
Bypass length decreases throughput
4
3000 μm 25 μm
Sensitive to high input pressures (violation of
Objective 2 possible)
5
4000 μm 25 μm
Sensitive to high input pressures (violation of
Objective 2 possible)
6
5000 μm 25 μm
Sensitive to high input pressures (violation of
Objective 2 possible), bypass length decreases
throughput
1 Note that, further details on the maximal possible pressure are provided later when possible
designs are explored using simulation.
45
trapping well would reverse the ratio and, therefore, would violate Objective 1
(Q trap > Q bypass , cf. Sect. 3.4.1).
Simulations reveal that this volumetric flow rate ratio between the trapping well
and the bypass channel increases when the bypass channel length is increased and/or
the gap width is increased (which is the case for all other specifications). However,
an increase of the bypass channel length also causes an increase of the time
that a droplet requires to pass this bypass. For example, the simulation showed
that, when increasing the bypass channel length from L bypass = 4000 μm to
L bypass = 5000 μm (using a gap width of w gap = 15 μm), the time that a droplet
requires to pass a single bypass increases from 0.25 to 0.32 s (which is an increase
of 28%). This effect adds up when multiple trapping wells are cascaded. When
additionally a certain upper limit for the loading time of droplets (i.e., especially
relevant for cells) has to be fulfilled, less trapping wells can be cascaded using a
longer bypass channel, which decreases the throughput.
On the other hand, the time for droplets to be trapped can be reduced by
increasing their speed, which can be achieved by applying higher pressures at the
inlets. Using the simulator allows to test different pressures for all six specifications
and the simulator predicts that the pressure is limited by Objective 2 (cf. Sect. 3.4.1).
More precisely, too high pressures at the inlets cause too high pressure gradients
between the trapping wells and the narrow gaps so that the condition described
in Eq. 3.13 is violated. This causes the trapped droplet to be pushed through the
two narrow gaps. The simulation shows that droplet speeds can be higher for the
prototypes which have a gap width of only 15 μm. This is because a smaller gap
width increases the Laplace pressure. 1
These simulation results now allow the designer to evaluate the robustness and
performance of the different specifications. Table 3.3 summarizes the obtained
insights. Based on these results, the designer can evaluate the specifications with
Table 3.3 Robustness evaluation
ID L bypass
w gap
Possible problems
1
3000 μm 15 μm
No robust volumetric flow rate ratio (violation of
Objective 1 possible)
2
4000 μm 15 μm
–
3
5000 μm 15 μm
Bypass length decreases throughput
4
3000 μm 25 μm
Sensitive to high input pressures (violation of
Objective 2 possible)
5
4000 μm 25 μm
Sensitive to high input pressures (violation of
Objective 2 possible)
6
5000 μm 25 μm
Sensitive to high input pressures (violation of
Objective 2 possible), bypass length decreases
throughput
1 Note that, further details on the maximal possible pressure are provided later when possible
designs are explored using simulation.